Daily Practice · Higher Plus
May 1990 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1990 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1990Write 5/(x - 1) + 3/(x + 1) as a single fraction.
- 2nd May 1990y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 3rd May 1990The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 4th May 1990A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 5th May 1990A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 6th May 1990x = 118 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th May 1990Solve 4x^2 + 19x - 5 = 0.
- 8th May 1990y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 4.
- 9th May 1990In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 10th May 1990The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 11th May 1990On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th May 1990A car covers 570 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th May 1990f(x) = 6x - 6. Work out the inverse function f^-1(x).
- 14th May 1990A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 15th May 1990In a vector proof you find that vector PQ = 3a + 5b and vector RS = 6a + 10b. What does this show about PQ and RS?
- 16th May 1990A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 17th May 1990A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 18th May 1990Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 19th May 1990Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 20th May 1990y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 21st May 1990A cuboid measures 8 cm by 12 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd May 1990A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd May 1990On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th May 1990Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 25th May 1990Use the iteration x(n+1) = cube root of (6x(n) + 5) with x(0) = 1. Work out x(1) to 3 decimal places.
- 26th May 1990y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 27th May 1990A cuboid measures 5 cm by 7 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th May 1990A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th May 1990A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 30th May 1990A rectangle is 9 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st May 1990Work out the nth term of the quadratic sequence 2, 10, 22, 38, ...